on each component of \({\Sigma }\) . One naturally has the notion of a
stratified-smooth family of holomorphic maps, and hence the
notion of a deformation, namely the germ of a family around the
central fiber together with an isomorphism of the central fiber with
the given map. Recall that a deformation is universal if any
other deformation is obtained from it by pullback, in a unique way, by
a map of parameter spaces. A holomorphic map \({u}: {\Sigma }\rightarrow X\)  is regular if the linearized Cauchy-Riemann operator is
surjective. The following theorem is the result of the well-known
gluing construction for holomorphic maps, c.f. Ruan-Tian [1]}
or the text McDuff-Salamon [2]} in the case of
genus zero:
